Inferential Statistics Part 1
larger samples of means will produce more normal distributions, closer to the population than smaller samples.
Central limit theorum demonstrates larger populations size do what overall smaller population sizes?
sample characteristics
Because population parameters are not known, _____ _________ are used in the place of parameters
Properly conservative for overall experiment-wise probability (.05) • Too conservative for individual contrasts (.0125)
Bonferroni Correction for alpha slippage is too conservative for what, and properly conservative for what?
Yes
Do sample means differ routinely?
Only provides support because at best we base our decision and inferences on probability
Does statistics prove anything?
Theoretical distribution of sampling means
This depicts the hypothetical distributions of X numbers of drawn samples, each producing its own mean.
Probability is 10/20 or .50 that a black sock would be drawn on a single attempt
What is the probability of drawing one black sock out of a drawer with 10 black socks and 10 blue socks?
Sampling Error
What is the random variation within and between samples as a result of individual differences and less than perfectly accurate point estimates?
(PA) up r (probability of something, then multiply number of times) (Coin .5 probability, 4 times=coin up 4)
What is the rule for the multiplication rule of probabilities for independent events?
Standard error of the mean
What is the standard deviation of a hypothetical distribution of sampling means, used to determine whether respective means differ significantly from each other?
SeMean
What is the standard deviation of the sampling distribution of means (s/√N)?
is the standard deviation of a hypothetical distribution of sampling means, used to determine whether respective means differ significantly from each other. Sample Mean.
What is the standard error of the mean and what creates it?
The amount of variability among the sample means in a sampling distribution of the means; standard deviation of the distribution of sample means drawn = σ/√N (e.g., σ =10; 25 samples drawn = 10/√25 = 10/5 = 2)
What is the standard error of the mean?
Probability theory
Inferential statistics is based in what?
(PA)r = . 52 = (.5 * .5) = .25 (R meant to up be up, like a power)
Multiplication Rule of Probabilities for Independent Events: What is the probability of flipping a coin and getting heads two consecutive times? What is the probability of flipping a coin and getting tails 3 consecutive times?
First Addition Rule of Probabilities (P A or B) = (PA) + (PB) = (Add both outcomes together, divide by total number) White = 3/10; Red = 5/10 Red or White = 3/10 + 5/10 = 8/10 or .8
Mutually Exclusive Compound Event: (What is the formula)? What is the probability that an object is white or red? An urn has 2 red and 3 white balls and 3 red and 2 black cubes inside.
Estimated SE mean
is based on the estimated population standard deviation (i.e., sample standard deviation and number of sample size) semean = s/√N
Number of occurrences of an event, divided by the total number of possible events.
What is the probability formula?
Confidence intervals
A range of score values expected to contain the value of μ at a given level of confidence (e.g., 95% confidence)
5 Red objects out of 10 possible objects; 5/10 = .5 • Probability of selecting a Black Cube?
An urn has 2 red and 3 white balls and 3 red and 2 black cubes inside. What is the probability of any object in the urn is red? What is the formula?
create hypothetical distributions that have their own SHAPES and STANDARD DEVIATIONS, but they differ standard Error of the Mean.
Sample means create what? Do they differ from standard error of means? Do they follow a normal distribution?
Sampling Error
Sample means differ routinely due to.....
is based on the estimated population standard deviation (i.e., sample standard deviation and number of sample size) semean = s/√N
What is estimated SE mean?
Divide the desired alpha level by the number of contrasts being made (e.g., .05/4) = .0125 (.0125) + (.0125) + (.0125) + (.0125) = .05
How do you find Bonferroni Correction for alpha slippage?
Making inferences about populations based on sample statistics
What is inferential statistics?
• one decision - - p < .05 • four decisions - - (.05) + (.05) + (.05) + (.05) = .20
If the probability of making an incorrect decision is .05, what is the probability of making at least one incorrect decision when four decisions must be made?
reduced confidence in decision-making that results from making multiple decisions (i.e., alpha slippage resulting from 'family-wise' error - aka experiment-wise error)
In statistics (e.g., t-tests) it is important to protect against?
probability that events would happen in a given manner (e.g., that two sample means would differ by a given amount)?
What is probability theory?
The random variation within and between samples as a result of individual differences and less than perfectly accurate point estimates.
What is sampling error?
As sample size increases, the sampling distribution of the mean approaches a normal distribution
What is the central limit theorum?
semean = s/√N
What is the formula for SE mean?
0
What is the mean of random error distributions?
A range of score values expected to contain the value of μ at a given level of confidence (e.g., 95% confidence)
What are confidence intervals?
+/- 1 SEMEAN = 68% of the means in the sampling distribution +/- 2 SEMEAN = 97% of the means in the sampling distribution +/- 3 SEMEAN = 99% of the means in the sampling distribution
What are the standard error of the mean intervals? (+/-1,2,3)
Obtained sampling mean and the Semean
What can be used to create confidence intervals?
Sample size goes up, variability goes up, sampling error does down, confidence goes up. Want a big sample, generalizes to population
What happens as sample size goes up? Why do you want a big sample?